We consider a multi-source network with a common monitor, where fresh updates are generated at each source, following a Poisson process. At any time, at most one source can transmit its update to the monitor, and transmission time for updates of each source follows some general distribution. The goal is to find a causal scheduling policy such that at any time, the latest update available at each source is fresh. In this paper, we quantify freshness using the age of information (AoI) metric, and propose a randomized policy, which we show is 3-competitive with respect to Pareto-optimal policies (that minimize the expected average AoI of each source). We also show that for a particular choice of the randomization parameter, the proposed randomized policy is 3-competitive with respect to an optimal policy that minimizes the weighted sum of the expected average AoI of all sources.